Prime numbers between 3201 and 3,300
There are 11 prime numbers between 3201 and 3,300: 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299.
How to work it out
- 1
A prime has exactly two factors, 1 and itself. To list them, cross out multiples of 2, then 3, then 5, and so on up to ā3300 ā 57.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 3201 and 3,300, with a total of 35,669.
- 3
The biggest gap between neighbouring primes in this range is 28, after 3271 (the next prime is 3299). There are 2 twin prime pairs (primes 2 apart): (3251, 3253), (3257, 3259).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,201 to 3,210 | 2 | 20% |
| 3,211 to 3,220 | 1 | 10% |
| 3,221 to 3,230 | 2 | 20% |
| 3,231 to 3,240 | 0 | 0% |
| 3,241 to 3,250 | 0 | 0% |
| 3,251 to 3,260 | 4 | 40% |
| 3,261 to 3,270 | 0 | 0% |
| 3,271 to 3,280 | 1 | 10% |
| 3,281 to 3,290 | 0 | 0% |
| 3,291 to 3,300 | 1 | 10% |
Questions
How many prime numbers are there between 3201 and 3,300?
11.
What is the biggest prime number below 3,300?
3299.
What is the first prime number after 3200?
3203.